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The Riemann problem for a pressureless hydrodynamic model is solved explicitly, whose solution is either a contact-vacuum-contact wave or a delta shock wave to connect the left and right constant states. Moreover, the global perturbed Riemann solutions for this model are also constructed by investigating carefully all the presentive delta shock interaction problems when the initial condition is made up of three piecewise constant states. Finally, the stability of Riemann solutions is also proved by letting the perturbed parameter tend to zero under this specially designated small perturbation of this step-like initial condition.

Interactions of delta shock waves in a pressureless hydrodynamic model